If my opponent is tapped out but has runes available for power, and conquers with a unit equipped with Last Rites, he has 11 cards in trash and chooses Rhasa from trash to summon from Last Rites conquer, if I use Disposal Order on 3 cards not choosing Rhasa and my opponent has no energy to play him because the trash now has 7 cards, what happens to Rhasa?

Rhasa is not played — it stays in the trash (or returns to it).

Your Disposal Order resolves first, dropping the trash to 8. When the Last Rites trigger resolves and your opponent plays Rhasa, Rhasa leaves the trash (7 cards left) and its cost is calculated then: 10 − 7 = 3 Energy + 1 Chaos Power. Since they're tapped out and can't pay the 3 Energy, the play fails the "all costs were paid" check, and the whole play is undone — Rhasa goes back to the trash (Rule 358.2, 358.5).

They can't swap to a different unit on that same trigger, and if they realize they can't pay before committing, they can simply decline the "may" — Rhasa just never leaves the trash. The cost is locked based on the trash count at the moment it's played, not what it was when they first named Rhasa (FAQ #8429).